9.M.3 A 2 × 2 matrix A is symmetric, and has eigenvalues 3 and --2. A 3-eigenvector is [35Find A. Hint: Because A is symmetric, you know that every -2-eigenvector is perpendicular toevery 3-eigenvector, which lets you find one. Then use the diagonalization theorem to describe Aas PDP-1

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Answered: 9.M.3 A 2 × 2 matrix A is symmetric,…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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9.M.3 A 2 × 2 matrix A is symmetric, and has eigenvalues 3 and -2. A 3-eigenvector is [3]. 5 Find A. Hint: Because A is symmetric, you know that every -2-eigenvector is perpendicular to every 3-eigenvector, which lets you find one. Then use the diagonalization theorem to describe A as PDP-¹.